This web site documents my 1999 summer research on a combinatorial design called the AntiMagic square. AntiMagic Squares are a variation on the heavily studied and wellunderstood magic square. In contrast, very little seems to be known about AMSs. These pages describe what was previously known about the structure and history of the AMS and also detail new discoverys regarding their enumeration and construction.
Thanks for your patience and understanding, as this page is still under construction!
 What is an AntiMagic Square?An AntiMagic Square (AMS) is an arrangement of the numbers 1 to n^{2} in a square matrix such that the row, column, and diagonal sums form a sequence of consecutive integers.^{ 1} The arrangement to the left is AntiMagic because sorting the sums (numbers in black on the border) yields the sequence: 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269 This is an example of an AMS(8), or AntiMagic Square of order 8, which comes from Madachy's Mathematical Recreations 
Given this definition, this research project aims to answer some of the following questions:
And of course, we aim to have fun doing it! After all this is classified as "Recreational Math!"
Table of Contents

A present day AntiMagic analogue to Durer's 1514 Magic Square 
Huge thanks go to my supervisor for the summer, Václav Linek
A research project funded by NSERC and The University of Winnipeg